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path integral is used for calculating work done by path dependent force like friction, so W can be replaced with path integral in that equation. for the difference in calculating path integral and regular integral see the below calculation another answer to John Cuthber, (on 30 Apr 2014 - 10:53 AM), take another approach to the problem. non conservative force like friction does not conserve mechanical energy. mechanical energy is PE and KE. consider a case in horizontal direction, then PE is out of the equation KE=1/2 mv^2= 1/2pv so if KE is not conserved then p is not conserved. If you are in objection with this . please explain with an example or give good reference link that explains this( it will be useful to many readers including me)

If you can not see the image of calculation got link https://sites.google.com/site/nonmassexpulsiontypethruster/contact Correct me if I am wrong if you can not view the image of calculation go to bottom of link https://sites.google.com/site/nonmassexpulsiontypethruster/contact correct me if I am wrong

[math]W =s*dp/dt[/math] rearranging [math]dp =(W/s)dt[/math] integrating both side [math]p =\int (W/s)dt[/math]

[math]p =\int Fdt[/math] [math]F =dp/dt[/math] [math]W =\int Fds[/math] [math]W =\int F*vdt[/math] [math]W =F*v*t[/math] [math]W =v*t*dp/dt[/math] [math]W =s*dp/dt[/math] This is how momentum and work are related(correct me if I am wrong). for Path dependence velocity v will be instantaneous velocity and delta change in arc length

friction is non-conservative or path dependent. if there is only conservative force why bother to call them conservative force not just force.The term conservative force comes from the fact that when a conservative force exists, it conserves mechanical energy. The most familiar conservative forces are gravity, the electric force (in a time-independent magnetic field), and spring force. A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if it meets any of these three equivalent conditions: 1. The curl of F is zero: 2. There is zero net work (W) done by the force when moving a particle through a trajectory that starts and ends in the same place: 3. The force can be written as the negative gradient of a potential Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not mathematically equivalent. For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl). Accordingly, some authors classify the magnetic force as conservative, while others do not. The magnetic force is an unusual case; most velocity-dependent forces, such as friction, do not satisfy any of the three conditions, and therefore are unambiguously nonconservative. I agree with F = dp/dt, or [math]p =\int Fdt[/math] (force is rate of change of momentum) But you can see that displacement (ds) can be changed to (vdt) by change of variables in integration, now the integration for calculating W will be with respect to time.Path integral is for calculating the work done by a non-conservative force

If constant path dependent force given along curved path, change in magnitude of velocity will be equal to change in magnitude of velocity by a same amount of path independent force along a straight line of length equal to curved path. However for path dependent force, x and y component of that tangential path dependent friction force will contribute in change in magnitude of velocity. So the x and y component (y component of less magnitude than that initial electromagnetic force, x component will be new without any cancelling initial force) will cause an equal and opposite reaction force on space craft. This will result in in some motion of space craft in oblique direction.

in a semi circular path, normal force will only change angular momentum. tangential force will change instantaneous velocity; Instantaneous velocity is always tangential to trajectory. Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity. Here is where path dependence and line integral comes; for path independent force, resultant force along chord and length of chord will give work done. since momentum is mass X velocity. that tangential force(friction) will reduce linear momentum. since friction will act against direction of motion, friction force is tangential along a curved path.

I assume that you can at-least agree that same magnitude of force in the direction of motion is required to start moving a ball from initial point to another point and that same Magnitude of force in opposite direction to motion is required to move ball from that point to stop the ball at original initial position. Since friction force will act against motion in opposite direction to that motion, at every point along that curved path friction force will act against motion and reduce velocity and there by momentum of the ball. Normal force in upper semicircular path will cause change in angular momentum. That angular momentum will be counter balanced by normal force given earlier in bottom semicircular path. If conservation of angular momentum is true in this case too. this will be dependent on path, if friction force is applied to stop the ball. the momentum transfer will be tangential along the path since it is against the direction of force exerted by second body. force is rate of change of momentum. friction force does negative work in most of the reference frames that's how they are connected

That's all true. but I am wrestling with those using path dependent nature of friction force, that's also a well established theory. Path independence means if work is done on a particle between 2 points over a path. Then distance of straight line joining those 2 points (displacement) and force applied in that direction is required to calculate the work done. but for path dependent force what happens in that path is also required. That's where line integral comes. Consider sketch below ; path independent force like electromagnetic force is applied on red line and path dependent friction force is applied over black curve. I assume that you can at-least agree that same magnitude of force is required to start moving a ball from initial point to another point and that same Magnitude of force is required to move ball from that point to stop the ball at original initial position. first some electromagnetic force is applied to move ball at rest from top left point to bottom end of red line. then friction force is applied along black curve to stop ball at top left point. Magnitude of friction force is magnitude of tangential force exerted on ball by tube along that black curved path. here both x component and y component of that tangential friction force act to stop the ball at top left point. so red line's force and black curve's force wont cancel each other. Then that resultant force will propel space craft in some oblique direction.

Action and reaction are equal and opposite but they act on different bodies. if action is on ball then reaction is on space craft. for eg: man jumping from a boat; if action is by man the reaction is on boat.. Let me explain my case . Ball and space craft gained momentum in equal and opposite direction by electromagnetic force in straight section. but then ball is brought into initial position and at rest with respect to space craft by path dependent friction force. for conservation of momentum to be true the ball has to be stopped by a straight force in opposite direction to the initial one. but for friction, force is in tangential direction along the curvilinear path. so both x and y component of that tangential force contribute to stop the ball at initial position with respect to space craft; so there would be an oblique force that will result in oblique movement of space craft. Remember I Don't want to move the ball to initial position and at rest in the earth's or any other reference frame but spacecraft's reference frame.

angular momentum and linear momentum are pseudo vectors , They are independently conserved. Our subject of interest is linear momentum. angular momentum only causes rotation around a point.

from well known equations you know that a non-zero work can produce non-zero change in momentum over distance. then nonzero work done by a path dependent force can change momentum of a Ball through a trajectory that starts and ends in the same place:. I mean for conservation of momentum to be true that work has to be zero so that there is no change in momentum. There is zero net work (W) done by the path independent force when moving a particle through a trajectory that starts and ends in the same place: for path independent force. its non -zero for path dependent force http://spiff.rit.edu/classes/phys211/lectures/power/power_all.html http://en.wikipedia.org/wiki/Conservative_force friction force is dependent on normal force and Mu( coefficient of friction) but friction force act on opposite direction of motion of that ball( that's tangential over a curve) . Correct me if I am wrong using technical explanations.

force is rate of change of momentum. if uniform force is applied over distance then momentum will increase continuously in equal steps in equal distance through the entire distance d. To brush up your memory on line integrals watch this video:- https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals/v/line-integral-example-1 work done by path dependent force is line integral or area between surface and path curve. In case of uniform force, area between flat surface and path curve Normal forces will increase friction. then it will be too complicated to calculate. You know Line integral itself is too tough to calculate. that's why I am asking for a proper software

I am not arguing with any body I am just discussing a feasibility of an invention. I am using well known theories of friction in physics to challenge another one in physics to the best of my knowledge please tell me where I am wrong or is there Any contradiction or either one of the theories has to be extended to fit the new situation. I will make my point clear here: assume 1 unit of force is required to generate 1 Unit of momentum. then In the first straight section 1 unit of force in "-ve Y" direction given for the distance of straight segment ( assume that length to be d) to generate 1 unit of momentum for the ball and ball then turns 180 degree reach the upper end of second straight tube . Assume arc length of semicircular arc is also equal to d. Then constant friction force is given in that curved tube on the ball. you know that only one unit of force in distance d is required to stop the ball. Since friction being path dependent limit of sum of tangent force in that semicircular arc in distance d is required to stop the ball ( here is where line integral comes - area under/ between curved path and a bottom plane) . For conservation of momentum to be true; one unit of force has to be given for same distance in y direction only to stop the ball . but for the path dependent force both x and y components of tangent friction force contribute to stop the ball.with respect to space craft. In that tangential friction force in semi circular arc,resultant of y component of force cancels out since that force applies in both up and down direction for equal distances( in first and second quadrant of arc). then we are left with x component of that tangent friction force and initial force in Y direction these forces will not cancel each other so there will be an oblique force acting on space craft. that force will result in propulsion of space craft in oblique direction.

I am explaining a simpler case; Assume ball and spacecraft has equal mass. ball is moved from upper end of left straight segment of tube to the bottom end of that straight tube using electromagnetic force. assume ball now has 1 unit of momentum in downward direction so spacecraft has 1 unit of upward momentum. and then ball turns 180 degree in the friction less bottom semicircular arc without losing velocity magnitude then ball now has 1 unit of momentum in upward direction vice-verse for space craft. ball then travels freely through right side straight tube; so no change in momentum for ball and space craft. then ball enters upper semicircular friction tube. in that friction tube friction force will act to make the momentum of ball to zero with respect to spacecraft. the friction being path dependent the vertical Momentum(M+y) of ball is made to zero by tangential force(Ft) in semicircular path ( line integral comes in to play in this case). my claim is that since Fx and FY contribute in tangential friction force (Ft) to make momentum (M+y) of ball zero with respect to space craft then some resultant force will be there on space craft to to propel it in any oblique direction. Is any such case could be true. Please be technical in answer; vague answer will not help anybody reading this forum. forget the friction tube mentioning in the below sketch its just one of many combinations possible

line integral of a closed path to be zero for just wiggle back and to.stays in original position. but friction does do some work in closed path so there must be equal and opposite reaction of that work resulting in thrust of space craft in any direction. can you suggest a good dynamic simulation software that uses line integrals or vector calculus; so that I can test this device in that software for all possible permutations and combinations to get a positive result before start building a actual prototype. help me in this regard

to prevent rotation, you can use another thruster that is mirror image (Mirror plane being vertical axis)of original thruster . So when two thrusters work simultaneously they cancel out lateral motion of space craft..

My inventions had won the attention and admiration of important persons from auto industry as well as scientific field, including editor of highly regarded international magazine ‘Engine Technology International’, Kajal Gupta of NASA, President of India (Dr. Abdul Kalam Azad - Renowned scientist in India), Director of Aeronautical Development Establishment (ADE) – A division of Defense Research and Development Organization (DRDO) - of India government, Director and Assistant Director (engines) of Vehicle Research and Development Establishment (VRDE) – A division of Defense Research and Development Organization (DRDO) - of India government, Brian Pereira - editor of highly regarded international magazine ‘Chip’, professors of Cochin University of Science and Technology , etc. A Technical article on one of my concept engine was published in highly regarded magazine ‘Engine Technology International’ I am sending an extract from magazine as attachment. For complete magazine go to the link (page 48) http://viewer.zmags.com/publication/9dd391bd#/9dd391bd/1 However I want to do some thing useful to humans and environment; that's why I came up with these medical inventions. but funding of these research is the problem. I contacted Monsanto and Glaxo (GSK). only Monsanto replied, asking me to submit resume. Can you suggest which organization should I contacted for these projects to be done. I am not asking for funding but I am also willing to do these as internal research of any relevant companies.

Here is non-mass expulsion type device, which uses properties of line integral and path dependent nature of friction force. The new device can achieve near light speed using properties inherent to relativity. In cases like LHC while particle moves at light speed the force is applied from stationary. But in new device force applied from and space craft is in same inertial frame, so comparatively less energy is required to attain light speed. Details of new device are given in link https://sites.google.com/site/nonmassexpulsiontypethruster/ Please comment your views on feasibility of the above concept for a Path independent force or conservative force work done in a closed path or its line integral must be zero.vice verse for path dependent force like friction. if friction of ball in closed path can do some work then there is equal and opposite reaction of that work done on space craft resulting in motion of space craft according to third law of motion by newton. share your thoughts on this can you suggest a good dynamic simulation software that uses line integrals or vector calculus; so that I can test this device in that software for all possible permutations and combinations to get a positive result before start building a actual prototype. help me in this regard

Which of following Inventions of mine are novel; and which one I should be working on as soon as possible Other concepts 1.) Make a large scale electro-mechanical-chemical device that mimic a bacteria's digestive system to undertake waste management including toilet waste 2.) Make a large scale electro-mechanical-chemical device that mimic a earthworm’s digestive system to produce organic fertilizer in large quantities 3.) Make a large scale electro-mechanical-chemical device that mimic a membrane that only let through water for high speed water purification. Create a model of growing humans from a cell – first cells are just divided and bonded together just as particles in 3D animation uses DNAs signals to control the growth once organs are formed organ level abstraction is made then organs are grown as whole and functions of organs are assumed to be performed as a whole. Bones and bone marrow are separate entities and muscles just perform their physical applications, just like muscles and bones in 3D animation software. Blood is modeled as fluid passes through veins and at organs or cells level abstract models are made. Nerves are modeled as electric conductors transferring control signals to different organs. Using this method Laser and sonic treatment (noninvasive) Lasers of two different wavelength are focused onto a fresh wound ( pressure is applied)and make the interference of waves cause a stimulation in cell’s molecules allowing them to chemically bond together for a quickest heal. http://www.hamamatsu.com/us/en/news/development/20131105000000.html http://www.popsci.com/technology/article/2010-08/mit-glucose-meter-checks-blood-sugar-levels-painless-ir-light Ultra sonic cleansing of body organs like lungs and fat depositions in blood veins and similar application even laser can be used for same application Two or more sonic waves focused on desired location and superposition along with Doppler effect can be used to resonate desired organs like lungs or veins walls and cleansing of accumulated waste like fat in veins can be done. Process is to throw off waste from walls using resonance or aggressive vibration. Then remove it from body by forced ventilation in case of lungs and external filtering fats from blood from the nearest point in a vein in treatment. For fats in blood vein we can use lasers to convert those fats to harmless substances that are soluble or miscible in blood. Cavitation too can be used if possible in safely manner; Cavitation can be described as the vibration of water and liquid detergent molecules using a very intense sound at high frequency, and could be simplified as ‘cold boiling’. New medicine system Use inhibitors and retarders or accelerators to inhibit retard or promote a chemical reaction that may be the cause of the decease or bad medical condition. For example use fermentation inhibitors to cure cancer- fermentation is the process to produce energy in cancerous cells. Other human cells mechanism is different.